Refinement of convergence rate for the strong law of large numbers in Banach space

DOI10.1080/17442508.2014.883078zbMath1337.60010OpenAlexW2063749878MaRDI QIDQ2811113

Aurel Spătaru, De Li Li

Publication date: 10 June 2016

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442508.2014.883078

zbMATH Keywords

strong law of large numberspartial sums of i.i.d. Banach space-valued random variablesHsu-Robbins-Erdős-Spitzer-Baum-Katz complete convergence theorem

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (1)

Complete moment convergence for Sung's type weighted sums of \(B\)-valued random elements

Cites Work

• Improved convergence rates for tail probabilities for sums of i.i.d. Banach space valued random vectors
• On the maximum sequence in a critical branching process
• Inequalities for B-valued random vectors with applications to the strong law of large numbers
• Complete convergence and almost sure convergence of weighted sums of random variables
• Strengthening classical results on convergence rates in strong limit theorems
• Refinement of convergence rates for tail probabilities
• Characterization of LIL behavior in Banach space
• A maximum sequence in a critical multitype branching process
• Tail probabilities for sums of independent Banach space valued random variables

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